Bernstein operators in Chebyshev spaces
Résumé
We explain why, on a given interval $[a,b]$, each Extended Chebyshev space possesses infinitely many Bernstein type operators, and we analyse how to build such operators. This study mainly makes use of some results on Extended Chebyshev spaces motivated by geometric design purposes which can now be considered classical. The question of convergence arises whenever we are faced with an infinite nested sequence of Extended Chebyshev space on $[a,b]$. We illustrate this with a few examples and we also briefly consider the case of Extended Chebyshev Piecewise spaces and Quasi Extended Chebyshev spaces.